The Magpies had lost the services of goalkeeper Bartosz Bialkowski in the first-half when he was stretchered off after diving at the feet of Charlie MacDonald and taken to hospital after suffering a head injury.
Replacement, 19-year-old Fabian Speiss, proved an able deputy, pulling off a series of fine saves, but he was beaten twice in three minutes, first when David Mooney netted with a header and then Mathieu Baudry volleyed home from close range.
Although Jeff Hughes gave County a lifeline in the 77th minutes, the O's held out to claim their first win in five league matches.
"I'm gutted, but it's been a phenomenal run," Curle said. "We now have another three away games to play and it's a good opportunity to start another sequence .
"That away record has been absolutely fantastic and we are ready to start another run. We take a lot of pride in that run because it's down to a lot of hard work, dedication and commitment from the players.
"We put so many balls into their box, but we didn't get on the end of the ball in the killer area. When we got to the final third, we huffed and puffed but we didn't have that little bit extra we needed up front.
"We did create chances, but if we had shown just a bit more of a cutting edge in that final third, things might have been different. The two goals we conceded were disappointing.
"For the first, one of their players walked past two of our players and all of a sudden is on the edge of our box and we've conceded.
"The second goal, we've failed to defend a ball into the middle of our box when people lost their runners. We gave them jobs to do marking in the danger area and if you fail, someone marches in and scores, which is what happened."